A force of attraction between any two objects with mass?

I'm having trouble grasping some of the text in my textbook. In addition to proposing that objects (and the earth) fall because they are attracted by a force, Newton apparently claimed "that there is a force of attraction between any two objects with mass." Einstein went on to suggest "that the force of attraction between two objects is due to the mass causing the space around it to curve."

Well if I'm on the beach and drop a rock in the sand next to a seashell, I can see how this would work. But if the seashell is a mile down the shore and I drop the rock I don't understand how it would attract the second object towards itself or vise versa. After some distance, their forces would dissipate. Wouldn't they?

Staff: Mentor

But if the seashell is a mile down the shore and I drop the rock I don't understand how it would attract the second object towards itself or vise versa. After some distance, their forces would dissipate. Wouldn't they?

The force between two masses falls off inversely with the square of the distance. So sure, the force from that seashell a mile away won't amount to much, but it's still there.

Staff: Mentor

The object's weight continually dissipates until it collides with the other object's dissipating weight.

An object's weight usually means the gravitational force exerted on it by the earth. So that doesn't dissipate.
The gravitational force that two objects exert on each other gets smaller with increasing distance, following an inverse square law.

An object's weight usually means the gravitational force exerted on it by the earth. So that doesn't dissipate.
The gravitational force that two objects exert on each other gets smaller with increasing distance, following an inverse square law.

Right, so if I take two objects that are 16 miles apart, their force is the smallest in the middle, but it will never become zero. The number is found by squaring the distance between them.

When the two objects are 16 miles apart, there is a certain gravitational force between them. Let's call that force F. Now if you move them so they are 8 miles apart, reducing the distance by a factor of 2, the strength of the force between them quadruples to 4F. Similarly, if you move them so they are 32 miles apart, increasing the distance by a factor of 2, the strength of the force between them reduces by a factor of 4 to become F/4.